Nearly inviscid faraday waves in slightly rectangular containers

In the weakly inviscid regime parametrically driven surface gravity-capillary waves generate oscillatory viscous boundary layers along the container walls and the free surface. Through nonlinear rectification these generate Reynolds stresses which drive a streaming flow in the nominally inviscid bulk; this flow in turn advects the waves responsible for the boundary layers. The resulting system is described by amplitude equations coupled to a Navier-Stokes-like equation for the bulk streaming flow, with boundary conditions obtained by matching to the boundary layers, and represents a novel types of pattern-forming system. The coupling to the streaming flow is responsible for new types of secondary instabilities of standing waves leading to chaotic dynamics, and in appropriate regimes can lead to the presence of relaxations oscillations. These are present because in the nearly inviscid regime the streaming flow decays much more slowly than the waves, and resemble a class of oscillations discovered by Simonelli and Gollub in a domain with an almost square cross-section. (author)